In this paper, we present several conditions for the existence of a Lagrange multiplier or a weak saddle point in multiobjective optimization. Relations between a Lagrange multiplier and a weak saddle point are establ...
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In this paper, we present several conditions for the existence of a Lagrange multiplier or a weak saddle point in multiobjective optimization. Relations between a Lagrange multiplier and a weak saddle point are established. A sufficient condition is also given for the equivalence of the Benson proper efficiency and the Borwein proper efficiency.
Owing to the wind and photovoltaic (PV) potential in Brazil, the country has recently seen increased exploration into the construction of wind-PV hybrid plants. However, as specific criteria for contracting this type ...
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Owing to the wind and photovoltaic (PV) potential in Brazil, the country has recently seen increased exploration into the construction of wind-PV hybrid plants. However, as specific criteria for contracting this type of project have not yet been developed, this paper presents a model to assist the government in contracting projects that maximize the socioeconomic well-being of the Brazilian electricity sector. For this, multiobjective programming is used to simultaneously handle two objective functions-maximally reducing emission density and minimizing the levelized cost of electricity (LCOE)-with the aid of the mixture arrangement technique. In this respect, the optimization method called normal boundary intersection (NBI) is applied to solve the multiobjective problem and construct the Pareto frontier. Additionally, a metric based on the ratio between entropy and the global percentage error (GPE) is used to identify the optimal Pareto solution. The model was applied to determine optimal configurations for wind-PV powerplants in twelve Brazilian cities, and the results obtained reveal the capacity of the model to indicate the optimum configuration according to the wind and PV potential of each city.
In the multiobjective programming literature, the concavity of the objectives is usually assumed to be a sufficient condition in seeking Pareto-optimal solutions. This paper investigates nondominated solutions associa...
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In the multiobjective programming literature, the concavity of the objectives is usually assumed to be a sufficient condition in seeking Pareto-optimal solutions. This paper investigates nondominated solutions associated with dominance cones via the assumption of the quasiconcavity of the objectives. Necessary as well as sufficient conditions for such quasiconcave multiobjective programming problems are obtained.
We present a proximal point method to solve multiobjective programming problems based on the scalarization for maps. We build a family of convex scalar strict representations of a convex map F from R(n) to R(m) with r...
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We present a proximal point method to solve multiobjective programming problems based on the scalarization for maps. We build a family of convex scalar strict representations of a convex map F from R(n) to R(m) with respect to the lexicographic order on R(m) and we add a variant of the logarithmic-quadratic regularization of Auslender, where the unconstrained variables in the domain of F are introduced in the quadratic term. The nonegative variables employed in the scalarization are placed in the logarithmic term. We show that the central trajectory of the scalarized problem is bounded and converges to a weak pareto solution of the multiobjective optimization problem.
In this paper, Lagrange multiplier theorems are developed for the cases of single-objective and multiobjective programming problems with set functions. Properly efficient solutions are also characterized by subdiffere...
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In this paper, Lagrange multiplier theorems are developed for the cases of single-objective and multiobjective programming problems with set functions. Properly efficient solutions are also characterized by subdifferentials and zero-like functions.
Using a theorem of Tijs, we derive results about approximate solutions for Nash equilibrium theory and for multiobjective problems. We describe conditions under which one can replace an infinite strategy set, an infin...
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Using a theorem of Tijs, we derive results about approximate solutions for Nash equilibrium theory and for multiobjective problems. We describe conditions under which one can replace an infinite strategy set, an infinite alternative set, or an infinite set of criteria by a finite subset without losing all approximate solutions of the problem under consideration.
In this paper, the vector exact l(1) penalty function method for nondifferentiable convex multiobjective programming problems is analyzed. The vector penalized optimization problem with the vector exact l(1) penalty f...
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In this paper, the vector exact l(1) penalty function method for nondifferentiable convex multiobjective programming problems is analyzed. The vector penalized optimization problem with the vector exact l(1) penalty function is defined. Conditions are given guaranteeing the equivalence of the sets of (weak) Pareto optimal solutions of the considered nondifferentiable multiobjective programming problem and of the associated vector penealized optimization problem with the vector exact l(1) penalty function. This equivalence is established for nondifferentiable vector optimization problems with convex functions. (C) 2012 Elsevier Inc. All rights reserved.
Airline network design encompasses decisions on an airline network shape and route flight frequencies. Related investigations handle the trade-off between enhancing passengers' service levels and lowering the airl...
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Airline network design encompasses decisions on an airline network shape and route flight frequencies. Related investigations handle the trade-off between enhancing passengers' service levels and lowering the airline's operating costs by applying deterministic optimization methods. In contrast with other conventional methods, Grey theory is a feasible mathematical device capable of forecasting airline traffic with minimum data and resolving problems containing uncertainty and indetermination. In the light of these developments, this study develops a series of models capable of forecasting airline city-pair passenger traffic, designing a network of airline routes and determining Eight frequencies on individual routes by applying Grey theory and multiobjective programming. A case study demonstrates the feasibility of applying the proposed models. Results in this study not only confirm the practical nature of the preposed models, but also their ability to provide high flexibility in decision making for airlines. (C) 2000 Elsevier Science B.V. All rights reserved.
The stability in the sense of semicontinuation for the cone efficient points and the cone weakly efficient points of a perturbation set in Banach space with perturbation order are studied. On this basis, the stability...
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The stability in the sense of semicontinuation for the cone efficient points and the cone weakly efficient points of a perturbation set in Banach space with perturbation order are studied. On this basis, the stability for the cone efficient solutions and the cone weakly efficient solutions of multiobjective programming problem under two perturbations are obtained in Banach space.
A class of second order (F, alpha, rho, d)-convex functions and their generalizations is introduced. Using the assumptions on the functions involved, weak, strong and strict converse duality theorems are established f...
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A class of second order (F, alpha, rho, d)-convex functions and their generalizations is introduced. Using the assumptions on the functions involved, weak, strong and strict converse duality theorems are established for a second order Mond-Weir type multi-obtive dual. (C) 2005 Elsevier Inc. All rights reserved.
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